Solve 1/4+2/x-7/4+3/x

$$1 / 4 + 2 / x - 7 / 4 + 3 / x$$

Evaluate

$$-\frac{3}{2}+\frac{5}{x}$$

Short Solution Steps

Since \frac{1}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-7}{4}+\frac{2}{x}+\frac{3}{x}$$

Subtract 7 from 1 to get -6.

$$\frac{-6}{4}+\frac{2}{x}+\frac{3}{x}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{2}+\frac{2}{x}+\frac{3}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply -\frac{3}{2} times \frac{x}{x}. Multiply \frac{2}{x} times \frac{2}{2}.

$$-\frac{3x}{2x}+\frac{2\times 2}{2x}+\frac{3}{x}$$

Since -\frac{3x}{2x} and \frac{2\times 2}{2x} have the same denominator, add them by adding their numerators.

$$\frac{-3x+2\times 2}{2x}+\frac{3}{x}$$

Do the multiplications in -3x+2\times 2.

$$\frac{-3x+4}{2x}+\frac{3}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and x is 2x. Multiply \frac{3}{x} times \frac{2}{2}.

$$\frac{-3x+4}{2x}+\frac{3\times 2}{2x}$$

Since \frac{-3x+4}{2x} and \frac{3\times 2}{2x} have the same denominator, add them by adding their numerators.

$$\frac{-3x+4+3\times 2}{2x}$$

Do the multiplications in -3x+4+3\times 2.

$$\frac{-3x+4+6}{2x}$$

Combine like terms in -3x+4+6.

$$\frac{-3x+10}{2x}$$

Factor

$$-\frac{\frac{1}{2}\left(3x-10\right)}{x}$$